The metro might work during the day but draws unsavory crowds at later times in the evening to the extend that its not safe, especially with luggage. Generally people, especially with luggage use an Uber or Bolt to get to the airport in normal countries also when public transport isn't anywhere close to your point of departure. Unfortunately the cost of taxis in Denmark makes it only available to only a very tiny part of society and Uber returning has done next to nothing for the disproportionally expensive taxi rates that stand no comparison to most other countries.